Which neural networks can be used only for storing and retrieving information?
Neural networks are usually trained to produce a certain output given a certain input. Often the output is a classification of the input or some other form of input description. Sometimes it is an action in a game and sometimes it is indeed stored data, a memory if you will. 

In that case the input is often a part of the stored data, so the NN actually completes the given input. This setup is called autoassociative memory, Hopfield networks are an example for this. 

In your example you might give this NN the first frame of the movie Avatar and it would output the complete movie. Unfortunately this would probably be absolutely crazy inefficient.